Despite keeper Allan McGregor being sent off after a clash with substitute Luciano De Bruno, after Barry Ferguson had scored Rangers' third goal, the Ibrox team continued to outplay Hapoel.
Rangers had taken the lead through Ferguson's powerful volley and went two up through top scorer Kris Boyd.
When Ferguson scored Rangers' third, the tie seemed all over but McGregor's sending off led to an anxious 15 minutes until substitute Charlie Adam slid home their fourth goal well into injury time.
Rangers looked in the mood from the start and Alan Hutton's glancing header was touched onto the bar by keeper Shavit Elimelech.
The home side's opening goal was well crafted. Chris Burke's pass found Nacho Novo and his cut-back was lashed high into the net by Ferguson.
A dreadful mistake by Yossi Abuksis led to Rangers' second goal. The midfield player lost possession on the edge of the box and Boyd slid his shot home despite protests from Hapoel that he used an arm.
Just before half-time Gavin Rae's volley was headed off the line by Baruch Dego.
Rangers added a third when Ferguson slid home Dado Prso's cross after good work by Hutton.
Stefan Klos replaced McGregor in goal, but Prso should have added to Rangers' lead before Adam notched their fourth goal.